Two of my relatives are studying musicology, and as I wanted to understand something of the subject but was not particularly interested in it, naturally I looked to obtain sources that concerned areas I am more interested in. The first surprise was finding a field I hadn't then heard of using some of the most advanced data analysis methods around. The second surprise was simply the discovery of a fascinating multi-disciplinary volume related to this subject:

Haas, R., & Brandes, V. (2010). Music that works: Contributions of biology, neurophysiology, psychology, sociology, medicine and musicology. Springer.

Another relevant book is Patel, A. D. (2010). Music, language, and the brain. Oxford university press

and as far as external or objective shared traits between music and math, see e.g.,

Yust, J., Wild, J., & Burgoyne, J. A. (Eds.). (2013). Mathematics and Computation in Music. Springer

or

Loy, G. (2011). Musimathics: the mathematical foundations of music (Vol. 1). MIT Press.

That said, there are not only some pretty significant issues with the study, the bbc's summary of it is even worse. It says nothing about math being beautiful any more than it does music. Rather, it purports to show that individuals who would tend to find certain mathematical formulae or equations elegant or inelegant do so using the same regions someone who appreciates poetry, sculptures, or death metal music would. In other words, if the methods were better it could conclude that the experience of beauty can change subjectively from person to person as we'd expect, but for any subject whatever their experience of beauty is will activate certain brain regions. The intent was to find the brain regions or neural correlates behind the general/universal experience of beauty and, to extent it shows anything more, it is neither related to music not math.

In order to answer such a question, we should I think consider the lateralization of the human brain, see e.g. http://en.wikipedia.org/wiki/Lateralization_of_brain_function. It seems that we have two categories of thinking: The Lefthemispere and the right hemisphere. Left is specialised, in logic, algebra, language, discrete, sequential time etc. Right is

specialised in phantasy, intuition, music, geometry, structural (Gestalt) perception, etc.

These essentially give two kinds of abstract thinking.

I am myself left-handed, therefore comparatively more right-brained but geometry is not one of my strengths (for now). However, language, music and intuition definitely are. And yet, human skills are being developed and the human brain is constantly being reprogrammed if we train it. I wonder to what extent (if ever) abstraction in math and music is similar.

Dear Hristina,

The brain woks in some dialectical way, combining the lest and right, through corpus callosum. Since you are left -handed, this means that the role of your hemispheres are reversed! May be this explains your lack of geometry.

As for the connection of music and mathematics, this is certainly a very important question. I think the best treatment (difficult) is Guerino Mazzola's book, The Topos of Music.Geometric Logic of Concepts, Theory,

and Performance, Bikhauser, 2002 Springer Basel AG.. More on Math and Music, download:

https://www.dropbox.com/s/zz9c1pv72k1mr5a/Math%20%26%20Music1.zip

https://www.dropbox.com/s/dn51lk85txmr54y/Math%20%26%20Music2.zip

I know that both hemispheres work together. Actually, some claim that there is a top/bottom brain distinction http://www.npr.org/blogs/13.7/2013/12/02/248089436/the-truth-about-the-left-brain-right-brain-relationship

I don't think there is only one explanation about what skills are dominant for a person. Even if we take left-handedness, there a lot of degrees of being left-handed. In general, there are a lot of genetic miracles which make us unique.

Two of my relatives are studying musicology, and as I wanted to understand something of the subject but was not particularly interested in it, naturally I looked to obtain sources that concerned areas I am more interested in. The first surprise was finding a field I hadn't then heard of using some of the most advanced data analysis methods around. The second surprise was simply the discovery of a fascinating multi-disciplinary volume related to this subject:

Haas, R., & Brandes, V. (2010). Music that works: Contributions of biology, neurophysiology, psychology, sociology, medicine and musicology. Springer.

Another relevant book is Patel, A. D. (2010). Music, language, and the brain. Oxford university press

and as far as external or objective shared traits between music and math, see e.g.,

Yust, J., Wild, J., & Burgoyne, J. A. (Eds.). (2013). Mathematics and Computation in Music. Springer

or

Loy, G. (2011). Musimathics: the mathematical foundations of music (Vol. 1). MIT Press.

That said, there are not only some pretty significant issues with the study, the bbc's summary of it is even worse. It says nothing about math being beautiful any more than it does music. Rather, it purports to show that individuals who would tend to find certain mathematical formulae or equations elegant or inelegant do so using the same regions someone who appreciates poetry, sculptures, or death metal music would. In other words, if the methods were better it could conclude that the experience of beauty can change subjectively from person to person as we'd expect, but for any subject whatever their experience of beauty is will activate certain brain regions. The intent was to find the brain regions or neural correlates behind the general/universal experience of beauty and, to extent it shows anything more, it is neither related to music not math.

I think it was Liam Hudson who wrote an interesting on thinking styles many years ago now in a book called Contrary Imaginations. I am not sure if this would give you any interesting background information for your work?

@Andrew: I would like to add a book to te books already cited by Andrew: Guerino Mazzola, The Topos of Music. Birkhauser. In this book the author uses the most advanced mathematics (Topos Theory, Algebraic Geometry, etc.) to express all the musical problems. The book is difficult, both from mathematics and/or music. But it is worth to be studied. In this book the tow modes of thinking are interrelated, and because of that it is interesting!

Thanks for the book recommendation! I will have to check it out.

Thank you for your contributions! I would really love to explore the links between music and geometry. The best scenario will be to wait for the appropriate moment when I will have the chance to study math-related sciences incl. geometry in a civilized country where people care about teaching and encourage curiosity as opposed to the current situation in my country where cheating & provincialism are rewarded. The lack of in-depth education does not hamper, however, the possibility to explore some of the books on the topic math-music.

I must say I'm still haunted by Sergio's thought that there is an infinity of types of abstract thinking. It sounds beautiful.

Here is an interview with Quincy Jones. It's not exactly on abstract thinking but he discusses certain interconnections between music, math and creativity

http://www.thedailyriff.com/articles/quincy-jones-a-three-sixty-human-being-451.php